Well what would be interesting is if - while he can't necessarily go back in his own timeline - he still was able to hit the past here and there - so it's feasible that he could "borrow" Bessie when he wasn't using it in his past incarnation.

That, to me, would be an interesting way to celebrate the 50th - have 11 basically go back through his previous 10 incarnations, maybe like there's something that was always "out of his sight" while he was doing something else and almost predestination. So maybe he needs to do something in Bessie, and Smith could always wear 3rd or 4th Doctor's wardrobe for it briefly. And go all the way back to the 1st.

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"Here you are in the club with your bottle full of Bud, you got grillz you got bling, but playa you don't know a thing..." Alice Cooper - Disco Bloodbath Boogie Fever